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Find all values of c ∈ C such that the linear transformation T ∈ L(C^3) given...

  1. Find all values of c ∈ C such that the linear transformation T ∈ L(C^3) given by T(z1,z2,z3)=(z1 +2z2 +2z3, −z2 +cz3, z3) is diagonalizable. For those values of c, find a basis of C^3 such that the matrix of T corresponding to that basis is diagonal.

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